An environmentally based growth model that uses finite difference calculus with maximum likelihood method: its application to the brackish water bivalve Corbicula japonica in Lake Abashiri, Japan Item Type article Authors Baba, Katsuhisa; Kawajiri, Toshifumi; Kuwahara, Yasuhiro; Nakao, Shigeru Download date 26/09/2021 19:27:52 Link to Item http://hdl.handle.net/1834/30882 14 Abstract—We present a growth analy­ An environmentally based growth model sis model that combines large amounts of environmental data with limited that uses finite difference calculus amounts of biological data and apply it to Corbicula japonica. The model uses with maximum likelihood method: the maximum-likelihood method with its application to the brackish water bivalve the Akaike information criterion, which provides an objective criterion for model Corbicula japonica in Lake Abashiri, Japan selection. An adequate distribution for describing a single cohort is selected from available probability density func­ Katsuhisa Baba tions, which are expressed by location Hokkaido Hakodate Fisheries Experiment Station and scale parameters. Daily relative 1-2-66, Yunokawa, Hakodate increase rates of the location parameter Hokkaido 042-0932, Japan are expressed by a multivariate logistic E-mail address: babak@fishexp.pref.hokkaido.jp function with environmental factors for each day and categorical variables indicating animal ages as independent Toshifumi Kawajiri variables. Daily relative increase rates Nishiabashiri Fisheries Cooperative Association of the scale parameter are expressed by 1-7-1, Oomagari, Abashiri an equation describing the relationship Hokkaido 093-0045, Japan with the daily relative increase rate of the location parameter. Corbicula japonica grows to a modal shell length Yasuhiro Kuwahara of 0.7 mm during the first year in Lake Hokkaido Abashiri Fisheries Experiment Station Abashiri. Compared with the attain- 31, Masuura, Abashiri able maximum size of about 30 mm, Hokkaido 099-3119, Japan. the growth of juveniles is extremely slow because their growth is less sus­ ceptible to environmental factors until Shigeru Nakao the second winter. The extremely slow Graduate School of Fisheries Sciences growth in Lake Abashiri could be a Hokaido University geographical genetic variation within 3-1-1, Minato, Hakodate C. japonica. Hokkaido 041-8611, Japan Extreme fluctuations, both short-term between environmental factors and and seasonal, in food availability (e.g. growth of filter feeders from field data. phytoplankton density) make it difficult Complex box models, such as eco­ to determine relationships between physiological models, can derive the the growth of filter-feeding bivalves relationships between environmental and environmental factors (Bayne, factors and the growth of filter-feeding 1993). However, it is becoming easier bivalves (Campbell and Newell, 1998; to acquire large amounts of environ­ Grant and Bacher, 1998; Scholten and mental data through the use of data Smaal, 1998). These models are useful loggers, submersible fluorometers, or for estimating impacts of cultivated remote-sensing satellites, which enable species on an ecosystem or the carrying environmental monitoring at daily or capacity of a species (or both) (Dame, subdaily intervals. The development 1993; Héral, 1993; Grant et al., 1993). of these devices could solve difficulties They are suitable for animals that have in data collection. However, analytical been widely studied, such as Mytilus methods that combine large amounts edulis, because they are derived by of environmental data with limited integrating a huge amount of ecophysi­ amounts of biological data (e.g. shell ological knowledge acquired mainly Manuscript approved for publication length) are not yet well developed. from laboratory experiments. However, 14 August 2003 by Scientific Editor. We present an environmentally based extrapolation of such knowledge to Manuscript received 20 October 2003 growth model that combines such natural conditions is still controver­ at NMFS Scientific Publications Office. unbalanced data sets. This model is sial (Jørgensen, 1996; Bayne, 1998). Fish. Bull. 102:14–24 (2004). useful in elucidating relationships Our model treats complicated eco- Baba et al.: An environmentally based growth model for juvenile Corbicula japonica 15 physiological processes as a black box; we constructed the parameter (dRIRL) is approximated by a sigmoid function model directly from fluctuations in environmental factors with environmental factors and animal ages as indepen­ and growth rates. Our approach is reasonable for animals dent variables; 3) Daily relative increase rate of the scale for which ecophysiological knowledge is limited, especially parameter is approximated by a simple function with the when the main purpose of investigation is to derive the dRIRL as an independent variable; 4) The model is opti­ relationships between environment and growth. mized by a maximum likelihood method; and 5) The best We applied the model to a single cohort of Corbicula model is selected by Akaike information criterion (AIC). japonica juveniles spawned in August 1997. We did not The AIC is an information-theoretic criterion extended consider any bias caused by adjacent cohorts because C. from Fisher’s likelihood theory and is useful for simulta­ japonica failed to spawn in 1995, 1996, and 1998 in Lake neous comparison of models (Akaike, 1973; Burnham and Abashiri owing to low water temperatures during the Anderson, 1998). spawning season (Baba et al., 1999). Such investigations provide important basic information, such as the shape of Study site and sampling method the distribution of a single cohort, and the relationship between growth rate and expansion rate of size variation To collect juveniles of C. japonica spawned in August 1997, in a single cohort. sediments were sampled with a 0.05-m2 Smith–McIntyre Corbicula spp. are harvested commercially in Japan. The grab once or twice a month from September 1997 to July annual catch ranged from 19,000 to 27,000 metric tons in 1999 at a depth of 3.5–4.0 m in Lake Abashiri (Fig. 1). The 1996 to 2000 (Ministry of Agriculture, Forestry and Fisher- habitat of C. japonica is restricted to areas shallower than ies1), of which C. japonica was the main species. Corbicula 6-m depth because the deeper area, the lower stratum of japonica is distributed in brackish lakes and tidal flats of the lake, is covered by anoxic polyhaline water.We assumed rivers from the south of Japan to the south of Sakhalin that the selectivity of the sampling gear on C. japonica (Kafanov, 1991), is a dominant macrozoobenthos in these juveniles was negligible because the gear grabs the juve­ lakes, and has important roles in bioturbation and energy niles with the sediment. Because the magnitude of spawn­ flow (Nakamura et al., 1988; Yamamuro and Koike, 1993). ing in 1997 was relatively small (Baba et al., 1999), we Juvenile C. japonica growth is fast in southern habitats. selected a sampling site where we found abundant settled Their spats collected in Lake Shinji, which lies in the south- juveniles in our preliminary investigations. Samples could ern part of its range, grow to a mean shell length of around not be obtained during winter because of ice cover. Sedi­ 6.7 mm in natural conditions by the first winter (Yamane et ments were washed with tap water on 2- mm and 0.125- al.2). In northern habitats, growth is also believed to be fast; mm mesh sieves from September 1997 to October 1998, Utoh (1981) reported that mean shell length at the first an­ and on 4.75-mm and 0.125-mm mesh sieves from April nual mark was around 5.7 mm in Lake Abashiri. In Utoh’s to July 1999. To separate the juveniles from the retained study differences between the shell lengths at the first an­ sediments, we treated the sediments with zinc chloride nual marks and the shell lengths of individuals aged to be solution as described by Sellmer (1956). Then we sorted one year were also reported. The purposes of the present the juveniles under a binocular microscope. Identification study are to elucidate juvenile growth and its relationship of the cohort spawned in 1997 was quite easy because C. to environmental factors in Lake Abashiri. japonica failed to spawn in 1995, 1996, and 1998 owing to low water temperatures during the spawning season (Baba et al., 1999). We considered all the individuals that passed Materials and methods through the larger-mesh sieves and that were retained on the smaller-mesh sieve as the 1997 cohort. Shell lengths Overview of the model were measured under a profile projector (V-12, Nikon Ltd., Chiyoda, Tokyo) at 50× magnification with a digital caliper Our model expresses relative growth rate for C. japonica by (Digimatic caliper, Mitsutoyo Ltd., Kawasaki, Kanagawa), a sigmoid function with environmental factors and animal which has a 0.02-mm precision. ages as independent variables. Modeling processes in gen­ eral follow five steps: 1) Shell lengths of a single cohort are Environmental factors summarized by an adequate probability density function, which is expressed by a location parameter and a scale Values for water temperature (°C), water fluorescence parameter; 2) Daily relative increase rate of the location (fluorescence equivalent to uranin density, µg/L), salinity (psu, practical salinity unit), and turbidity (equivalent to kaolin density, ppm) were obtained for 0.1-m intervals 1 Ministry of Agriculture, Forestry and Fisheries. 1996– 2002. Statistics on fisheries and water culture production. from unpublished data at the Abashiri Local Office of Association of Agriculture and Forestry, 1-2-1 Kasumigaseki, the Hokkaido Development Bureau.3 The variables were Chiyoda, Tokyo 100-0013, Japan. measured by a submersible fluorometer (Memory Chloro­ 2 Yamane, K., M. Nakamura, T. Kiyokawa, H. Fukui, and E. tec, ACL-1180-OK, Alec Electronics Ltd., Kobe, Hyogo) at Shigemoto. 1999. Experiment on the artificial spat collec­ four sites in Lake Abashiri at intervals of about one week tion. Bull. Shimane Pref. Fish. Exp. Stn., p. 232–234. Unpubl. rep. Shimane Prefectural Fisheries Experimental Station, (Fig.